How Enigma Worked

I can't be the only one who saw the imitation game and was disappointed that we weren't shown how Turing's machine worked. It turns out it was pretty complicated - but I can tell you how the German code maker Enigma worked - and a bit of what had to happen to crack it.

The Design:

Above is a stationary diagram of what an enigma engine would have looked like - let's start by examining one of the wheel shaped rotors.

There are 26 contacts with internal wiring that maps contacts to each other in such a way that if you send a signal down one contact it will go down the wire and out another.

The first step to cracking enigma was getting a hold of the designs for the device. This was done quite early in the war.

But of course there was more to this - there were several rotors in even the early edition of enigma, all wired together. Note that the wires connecting the rotors were stationary, so you could move the rotor such that its output connected to a different stationary input. Thereby connecting to a different input in the adjacent rotor.

After passing through all the rotors the signal would reach a stationary wheel - known as a reflector. The reflector would loop the signal back into the system (through a different contact) - the signal would pass through all of the rotors again, then go all the way back. This would repeat several times.

So the user would click on their keyboard and send signals through the machine - this would light a bulb corresponding to the new letter after several cycles of scrambling. To make it even more confusing for any codebreakers - the rotors would also move forward by one click every time a new keyboard key was pressed.

This might take a few re-readings to visualise, and we couldn't expect Nazi operators to remember all of this reliably. This would have made the system useless - because operators wouldn't be able to convert code back to German.

However you might have noticed that this process is reversible. If a wheel is designed such that a wire runs from A to Z, it's clear that inputting Z will spit out A. This also means that if A maps to K after many layers of scramblings, inputting K into an identical engine where the wheels all start in the same positions, would give you A. The second engine would also rotate every key-press, so the two calibrations would update in sync.

Hopefully you can see now that with the wiring inside the rotors combined with the wiring between them, you just have to turn the rotors and the same input would map to a different output - the diagram below gives an example of a possible input to output pathway.

Calibration + the ground setting:

The starting position of the rotors was decided on and changed everyday. Enigma would be set to this starting position at the beginning of every message.

But of course the other operators had to be informed of the new setting daily.

At the same time every morning, the positions of the rotors would be sent out as a string of characters representing which contacts were on the top of the rotors at the beginning of each message. This information was always coded with the same standard ground setting.

Perhaps you can see the weakness inherent in this system - every morning thousands of similar messages could be picked up - and all of them were coded the same way.

Adding the Plugboard:

Later a plugboard was added to enigma - this essentially connected the inputs of different letters. This a signal going through A for example could be redirected to go through D (or whatever letter was suitable). In some ways this served a similar role to another rotor - but one where the connections could be changed at will, so stealing the designs of the plugboard wouldn't help.

'Heil bloody Hitler'

This story kind of sounds like an urban myth and I was surprised to find that it was true. It wasn't enough to break Enigma on its own - but it is true that a lot of the messages picked up ended with these same 10 characters. It became possible to assume that the last 10 characters of any code were code for Heil Hitler or similar regular sign-offs. This made reverse engineering to find the initial set up much easier. So after all the work that went into designing it – Enigma was foiled in the end by basic human foolishness, and thus WWII was shortened by 2 years. Thank god for human incompetence.